Loop-defining algorithm

With reference to Fig. 7, Epp and Fowler (E2) gave the following description of their loop defining algorithm ... 

Third, we only aim at the synthesis of single-loop logic algorithms. In other words, we assume that the only loop is the one that is achieved in the schema by the recursion on the induction parameter, and that none of the instances of the predicate-variables is defined recursively (possibly as a divide-and-conquer logic algorithm). 

The gas turbine eontrol loop eontrols the Inlet Guide Vanes (IGV) and the Gas Turbine Inlet Temperature (TIT). The TIT is defined as the temperature at the inlet of the first stage turbine nozzle. Presently, in 99% of the units, the inlet temperature is eontrolled by an algorithm, whieh relates the turbine exhaust temperature, or the turbine temperature after the gasifier turbine, the eompressor pressure ratio, the eompressor exit temperature, and the air mass flow to the turbine inlet temperature. New teehnologies are being developed to measure the TIT direetly by the use of pyrometers and other speeialized probes, whieh eould last in these harsh environments. The TIT is eontrolled by the fuel flow and the IGV, whieh eontrols the total air mass... 

The performance and large-scale feasibility of a TN algorithm depend on the precise formulation of a truncation criterion and implementation of the inner PCG loop. The PCG process can be terminated when either one of the following conditions is satisfied (1) the residual rk is sufficiently small, (2) the quadratic model qk p ) as defined in Eq. [35] is sufficiently reduced, or (3) a direction of negative curvature d is encountered (i.e., < 0). A negative... 

The basic function of the algorithm is to implement a feedback control loop, as defined by the controller responsibilities, along with appropriate checks to detect internal or external failures or errors. 

A primary task in high-level architecture synthesis is the extraction of the data flow from a given algorithm description. The term data flow is defined here as the combination of operations and dependencies between them that define the algorithm. In contrast, control flow is then defined as a (partial) ordering of computations meeting the restrictions of their dependencies. The control flow is usually specified by introducing loops and function hierarchy. 

Figure 19.1 Diagram showing the arrangement for closed-loop learning control. Following a femtosecond laser pulse, the products of the photochemical process are detected and compared with the user-defined objectives stored on the computer. A learning algorithm then calculates the modified electric fields required to shape the laser pulse and further optimize the yield of the desired product. Cycling through the loop many times gives the optimum pulse shape and best product yield. Adapted from Brixner et o/, Chem. Phys. Chem., 2003, 4 418, with permission of John Wiley Sons Ltd...

Figure Al. The lowest level hierarchical structure for most quantum mechanical computational algorithms. The inner loop is used to converge the self-consistent field in order to establish the electronic structure to within a user-defined tolerance. The outer loop is used to optimize the structure to within a defined geometric tolerance.

Control algorithms We have discussed that in closed-loop control systems a corrective action is taken by the controller in response to feedback from a transducer. The exact corrective action depends on the algorithm which has been developed. The simplest control approach is a two position control which turns the control element on and off based on the monitored value of the output. With an on/off strategy, the process value will typically oscillate above and below the set point. The most common controller is the PID (proportional, integral, and derivative) loop controller which is able to detect an early trend, adjust quickly, and prevent an over-correction. A PID controller can maintain temperatures within 1°F. The controller provides the means to define the control algorithm by assigning a constant for each of the three control modes. Typically, most of the adjustment is accomplished with the proportional control element, with the control action, u be-... 

The array V has five elements. Each element of the array can be retrieved by an indexed variable. For example u(l) = 12, v 2) = 5, v 3) = 4, and so on. The for-to-do iteration scheme is used to repeat a sequence of instructions (for multiplication and for printing) five times. At each iteration of the for-to-do loop, the value of x is incremental and serves as an index to retrieve the values from the array. For instance, at the third iteration x = 3 and therefore v(3) = 4, which in turn is passed to the variable q. Next, r is the result from the multiplication of q by 10 this result is printed. It is assumed that the print(r) instruction is a subroutine defined elsewhere. When the five iterations are completed, the outcome of the algorithm will be the following values printed (either on the screen of the computer or on paper) 120, 60, 40, 80 and 20. 

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